1. Can the pilot steer the front wheel of the plane while on the ground in some way other than by using the engines?
2. If so, is this accomplished using the same yoke that steers the plane in flight?
3. If so, how does the pilot transfer between these two functions?
Typically, the pilot can steer the nosewheel with his rudder pedals while on the ground, but the slewing angle is limited to about plus and minus fifteen degrees.
"2. If so, is this accomplished using the same yoke that steers the plane in flight?"
For steering angles greater than about fifteen degrees, modern jet airplanes are equipped with a "tiller," which can steer the nosewheel up to an angle of about plus and minus 72 degrees. The yoke does not provide nosewheel steering input.
"3. If so, how does the pilot transfer between these two functions?"
While the plane is rolling out on the runway, it iis transitioning from aerodynamic (rudder) yawing to nosewheel steering. Large steering inputs are not desireable until the plane is in taxiing mode.
It looks to me like some ground crewman did not do a good job of re-attaching the steering links on the nosewheel after the pushback by the ground tractor. Without those links attached, the nosewheel is free to turn any way it wants to. The links may have come undone on the takeoff roll.